Answer:- 23.0 mg
Solution:- Radioactive decay obeys first order kinetics and the first order kinetics equation is:
[tex]lnN=-kt+lnN_0[/tex]
where, [tex]N_0[/tex] is the initial amount of radioactive substance and N is it's amount after time t. k is the decay constant.
From given information, Original amount, [tex]N_0[/tex] of the radioactive substance is 184 mg and we are asked to calculate the amount N after 15 days. It means, t = 15 days
Half life is given as 5 days. From the half life, we could calculate the decay constant k using the equation:
[tex]k=\frac{0.693}{t_1_/_2}[/tex]
where, [tex]t_1_/_2[/tex] is the symbol for half life. let's plug in the value of half like to calculate k:
[tex]k=\frac{0.693}{5days}[/tex]
[tex]k=0.1386day^-^1[/tex]
Let's plug in the values in the first order kinetics equation and solve it for N:
[tex]lnN=-0.1386day^-^1(15days)+ln184mg[/tex]
[tex]lnN=-2.079+5.215[/tex]
lnN = 3.136
[tex]N=e^3^.^1^3^6[/tex]
N = 23.0 mg
So, 23.0 mg of Bi-210 would be remaining after 15 days.
